Is $\Bbb R$ a splitting field over $\Bbb R$? Over $\Bbb Q$? What does this mean?

Question

There are two problems in Fraleigh's text on abstract algebra.

Which are true?

1.$\mathbb{R}$ is a splitting field over $\mathbb{R}$
2.$\mathbb{R}$ is a splitting field over $\mathbb{Q}$

I could not understand the questions. I know the definition of a splitting field of a polynomial over some field but here, no polynomial is mentioned.

Can someone help to understand the problem and the process of solving these types of problem?

Answer 1

Hints:

1. Can you think of polynomial with coefficient in $\mathbb{R}$ such that all of its zeros are in $\mathbb{R}$ as well?
2. The splitting field $L$ of a set of polynomials in $K[x]$ is gotten by adjoining all the zeros of those polynomials. Consequently $L/K$ is an algebraic extension.